If A + B + C = 180°, prove that 1. ...
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If A + B + C = 180°, prove that 1. sin 2 A + sin 2 B-sin2 C = 4 cos A cos B sin C 2. cos 2 A + cos2 B + cos2 C =-1 1

JEE/Engineering Exams
Maths
Solution
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( A+B+C=180^{circ} ) ( sin 2 A+sin 2 B-sin 2 C ) ( =2 sin A cos A+2 sin A cos B-2 sin C cos C ) We Rrow as ( A+B+C=180^{circ} ) A in supplement angle of ( B+C ) ( Rightarrow 2 sin (B+C) cos A+2 sin (A+C) cos B ) ( sin (A+B) cos C ) ( Rightarrow 2 sin B cos (2 cos B sin C) ) ( cos A ) ( +(2 sin A cos t+2 cos A sin C) cos B ) ( -(2 sin A cos B+2 cos A sin B) cos C ) ( 2 sin B cos (cos A+2 cos B sin C cos A) ) ( +2 sin A cos C cos B+2 cos A sin C log B ) ( -2 sin A cos B cos C-2 cos A sin B cos C ) ( 4 cos B sin C cos A )
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